4x+5=(12x+4)(5x+5)

Solution for 4x+5=(12x+4)(5x+5) equation:

4x+5=(12x+4)(5x+5)

We move all terms to the left:

4x+5-((12x+4)(5x+5))=0

We multiply parentheses ..

-((+60x^2+60x+20x+20))+4x+5=0


We calculate terms in parentheses: -((+60x^2+60x+20x+20)), so:

(+60x^2+60x+20x+20)

We get rid of parentheses

60x^2+60x+20x+20

We add all the numbers together, and all the variables

60x^2+80x+20

Back to the equation:

-(60x^2+80x+20)


We add all the numbers together, and all the variables

4x-(60x^2+80x+20)+5=0

We get rid of parentheses

-60x^2+4x-80x-20+5=0

We add all the numbers together, and all the variables

-60x^2-76x-15=0

a = -60; b = -76; c = -15;
Δ = b2-4ac
Δ = -762-4·(-60)·(-15)
Δ = 2176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-8\sqrt{34}}{2*-60}=\frac{76-8\sqrt{34}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+8\sqrt{34}}{2*-60}=\frac{76+8\sqrt{34}}{-120}
$